Precise Definition of Infinite Limits at Infinity: Example

in MES Science17 days ago

In this video I go over a useful example to better illustrate the precise definition of infinite limits at infinity. The example I go over is a math proof using the precise definition of the limit as x approaches infinity of the function f(x) = 1 + x3 and proving it is equal to infinity.

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Precise Definition of Infinite Limits at Infinity: Example

Example

Prove using the precise definition:

Solution

Recap on Precise Definition:

Let f be a function defined on some interval (a, ∞). Then:

means that for every positive number M there is a corresponding positive number N such that:

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